{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bilevel-approaches-for-learning-of","title":"Bilevel approaches for learning of variational imaging models","arxiv_id":"1505.02120","date":"2015-05-08","proceeding":null,"authors":["Luca Calatroni","Cao Chung","Juan Carlos De Los Reyes","Carola-Bibiane Schönlieb","Tuomo Valkonen"],"abstract":"We review some recent learning approaches in variational imaging, based on\nbilevel optimisation, and emphasize the importance of their treatment in\nfunction space. The paper covers both analytical and numerical techniques.\nAnalytically, we include results on the existence and structure of minimisers,\nas well as optimality conditions for their characterisation. Based on this\ninformation, Newton type methods are studied for the solution of the problems\nat hand, combining them with sampling techniques in case of large databases.\nThe computational verification of the developed techniques is extensively\ndocumented, covering instances with different type of regularisers, several\nnoise models, spatially dependent weights and large image databases.","url_abs":"http://arxiv.org/abs/1505.02120v1","url_pdf":"http://arxiv.org/pdf/1505.02120v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"bilevel-approaches-for-learning-of","repo_url":"https://github.com/dvillacis/bilevel_toolbox","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}